Problem 1
\(\mathrm{T} / \mathrm{F}: \int \sin ^{2} x \cos ^{2} x d x\) cannot be evaluated using the techniques described in this section since both powers of \(\sin x\) and \(\cos x\) are even.
Problem 1
Fill in the blank: Partial Fraction Decomposition is a method of rewriting ___________ functions.
Problem 1
Substitution “undoes” what derivative rule?
Problem 1
T/F: Integration by Parts is useful in evaluating integrands that contain products of functions.
Problem 1
Evaluate the indefinite integral to develop an understanding of Substitution. $$ \int \frac{e^{\sqrt{x}}}{\sqrt{x}} d x $$
Problem 2
\(\mathrm{T} / \mathrm{F}:\) One can use algebra to rewrite the integrand of an integral to make it easier to evaluate.
Problem 2
T/F: It is sometimes necessary to use polynomial division before using Partial Fraction Decomposition.
Problem 2
If one uses Trigonometric Substitution on an integrand containing \(\sqrt{25-x^{2}}\), then one should set \(x=\) ____________.
Problem 2
T/F: Integration by Parts can be thought of as the "opposite of the Chain Rule."
Problem 2
The hyperbolic functions are used to define points on the right hand portion of the hyperbola \(x^{2}-y^{2}=1,\) as shown in Figure \(6.6 .1 .\) How can we use the hyperbolic functions to define points on the left hand portion of the hyperbola?
